Question

The wave function for a traveling wave on a taut string is (in SI units) y(x,t) = 0.380 sin (5πt − 4πx + π 4)

(a) What are the speed and direction of travel of the wave?

speed

________ m/s direction(positive-x, positive-y, positive-z, negative-x, negative-y, negative-z)

(b) What is the vertical position of an element of the string at t = 0, x = 0.120 m?
_______m

(c) What is the wavelength of the wave?
_______m

(d) What is the frequency of the wave?
______Hz

(e) What is the maximum transverse speed of an element of the string?
_______m/s

Answer 1

The wave function is given by
  
And comparing with the given values, we get
   
a)
  The speed of the wave is
     
And as the phase contains the form , so, the direction of speed is in the positive x direction.

b)

So, at t = 0, x = 0.120 m, the displacement is
  
  

c)

The wavelength of the wave is
  

d)

The frequency of the wave is
     

e)
The maximum transverse speed is